Hookes law equation for all gauges of copper wire

[groom03]

[SOLVED] Hookes law equation for all gauges of copper wire

Homework Statement

For my coursework I'm trying to find an equation using hookes law that works with all gauges of copper wire, i know that this means i will have to change the hookes law equation from F=ke to F=ake (a is not the area it's just a letter for the constant that i need to find)

Homework Equations

F=ke
F=ake
Youngs modulus

The Attempt at a Solution

i've tried working out the stiffness for several wire gauges and seeing if there was a pattern to them but my teacher said i should involve the youngs modulus equation.

Any help really appreciated

 

[Hootenanny]

Hooke's law can be derived by collecting the constants of Young's modulus. Try doing the same, but this time you want two constants, not just one.

 

[groom03]

by substituting i can get E=kl/A

A is going to be known because i'd know the wire gauge and using rho=f/a i can work out the force but i still can figure out how i'd find k unless i'd already know it when working out

Am i getting close?

 

[Hootenanny]

Young's modulus in it's entirety is defined thus,

E = \frac{\sigma}{\varepsilon}= \frac{F/A_0}{\Delta \ell/\ell_0} = \frac{F \ell_0} {A_0 \Delta \ell}

Where F is the applied force, A_0 is the original area, \Delta\ell is the extension, \sigma is the stress and \varepsilon is the strain.

Does that help?

 

[groom03]

scratch that i can also get the equation k=EL/A but now I'm totally stuck

i could substitute that k into the f=ke equation but I've been told that the youngs modulus was for a unit length so i would have to do something to...

 

[Hootenanny]

What's wrong with,

F = \frac{A_0E\Delta\ell}{\ell_0} = A_0\cdot C\Delta\ell

 

[groom03]

What's wrong with,

F = \frac{A_0E\Delta\ell}{\ell_0} = A_0\cdot C\Delta\ell

i think I've figured out how you get to that

E=FL/Ae

EA=FL/e

EAe=FL

EAe/L=F

F=ACe (if C equals youngs mod/length)

Which rearranges to e=F/A/C

i think that's right... i hope

 

[Hootenanny]

i think I've figured out how you get to that

E=FL/Ae

EA=FL/e

EAe=FL

EAe/L=F

F=ACe (if C equals youngs mod/length)

Which rearranges to e=F/A/C

i think that's right... i hope

Yup, sounds good to me

 

[groom03]

YAAAAAAAAY

thanks for your help